Abstract
Complex beams play important roles in wireless communications, radar, and satellites, and have attracted great interest in recent years. In light of this background, we present a fast and efficient approach to realize complex beams by using semidefinite relaxation (SDR) optimization and amplitude-phase digital coding metasurfaces. As the application examples of this approach, complex beam patterns with cosecant, flat-top, and double shapes are designed and verified using full-wave simulations and experimental measurements. The results show excellent main lobes and low-level side lobes and demonstrate the effectiveness of the approach. Compared with previous works, this approach can solve the complex beam-forming problem more rapidly and effectively. Therefore, the approach will be of great significance in the design of beam-forming systems in wireless applications.
摘要
复杂波束在无线通信、 雷达和卫星等领域发挥着重要作用, 近年来引起人们的极大兴趣. 在此背景下, 提出一种利用半定松弛优化和幅相数字编码超表面实现复杂波束的快速有效方法. 作为该方法的应用实例, 设计了具有余割、 平顶和双峰形状的复杂波束, 并通过全波模拟和实验测量进行了验证, 结果具有良好的主瓣和副瓣性能, 证明了该方法的有效性. 与以往工作相比, 该方法可以更快、 更有效地解决复杂的波束形成问题, 对无线应用中波束形成系统的设计具有重要意义.
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
References
Balanis CA, 2011. Modern Antenna Handbook. John Wiley & Sons, Hoboken, USA.
Bao L, Wu RY, Fu XJ, et al., 2019. Multi-beam forming and controls by metasurface with phase and amplitude modulations. IEEE Trans Antenn Propag, 67(10):6680–6685. https://doi.org/10.1109/TAP.2019.2925289
Boyd S, Vandenberghe L, 2004. Convex Optimization. Cambridge University Press, Cambridge, USA.
Bucci OM, D’Elia G, Mazzarella G, et al., 1994. Antenna pattern synthesis: a new general approach. Proc IEEE, 82(3):358–371. https://doi.org/10.1109/5.272140
Bucci OM, Caccavale L, Isernia T, 2002. Optimal far-field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions. IEEE Trans Antenn Propag, 50(11):1539–1554. https://doi.org/10.1109/TAP.2002.803959
Caorsi S, Massa A, Pastorino M, et al., 2005. Optimization of the difference patterns for monopulse antennas by a hybrid real/integer-coded differential evolution method. IEEE Trans Antenn Propag, 53(1):372–376. https://doi.org/10.1109/TAP.2004.838788
Cui TJ, Liu S, Zhang L, 2017. Information metamaterials and metasurfaces. J Mater Chem C, 5(15):3644–3668. https://doi.org/10.1039/C7TC00548B
Dolph CL, 1946. A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level. Proc IRE, 34(6):335–348. https://doi.org/10.1109/JRPROC.1946.225956
Fazel M, Hindi H, Boyd S, 2004. Rank minimization and applications in system theory. Proc American Control Conf, p.3273–3278. https://doi.org/10.23919/ACC.2004.1384521
Grant M, Boyd S, 2020. CVX: Matlab Software for Disciplined Convex Programming, Version 2.2. http://cvxr.com/cvx [Accessed on Jan. 30, 2020].
Kajenski PJ, 2012. Phase only antenna pattern notching via a semidefinite programming relaxation. IEEE Trans Antenn Propag, 60(5):2562–2565. https://doi.org/10.1109/TAP.2012.2189709
Khodier MM, Christodoulou CG, 2005. Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization. IEEE Trans Antenn propag, 53(8):2674–2679. https://doi.org/10.1109/TAP.2005.851762
Lebret H, Boyd S, 1997. Antenna array pattern synthesis via convex optimization. IEEE Trans Signal Process, 45(3):526–532. https://doi.org/10.1109/78.558465
Li JY, Qi YX, Zhou SG, 2017. Shaped beam synthesis based on superposition principle and Taylor method. IEEE Trans Antenn Propag, 65(11):6157–6160. https://doi.org/10.1109/TAP.2017.2754468
Liang JC, Cheng Q, Gao Y, et al., 2022. An angle-insensitive 3-bit reconfigurable intelligent surface. IEEE Trans Antenn Propag, 70(10):8798–8808. https://doi.org/10.1109/TAP.2021.3130108
Lou Y, Jin L, Wang HM, et al., 2023. Multi-stream signals separation based on space-time-isomeric (spatio) array using metasurface antenna. Sci China Inform Sci, early access. https://doi.org/10.1007/s11432-023-3788-y
Luo ZQ, Ma WK, So AMC, et al., 2010. Semidefinite relaxation of quadratic optimization problems. IEEE Signal Process Mag, 27(3):20–34. https://doi.org/10.1109/MSP.2010.936019
Nai SE, Ser W, Yu ZL, et al., 2010. Beampattern synthesis for linear and planar arrays with antenna selection by convex optimization. IEEE Trans Antenn Propag, 58(12):3923–3930. https://doi.org/10.1109/TAP.2010.2078446
Palacios J, De Donno D, Widmer J, 2016. Lightweight and effective sector beam pattern synthesis with uniform linear antenna arrays. IEEE Antenn Wirel Propag Lett, 16:605–608. https://doi.org/10.1109/LAWP.2016.2594092
Shi L, Deng YK, Sun HF, et al., 2012. An improved real-coded genetic algorithm for the beam forming of spaceborne SAR. IEEE Trans Antenn Propag, 60(6):3034–3040. https://doi.org/10.1109/TAP.2012.2194642
Strang G, 2023. Introduction to Linear Algebra. Wellesley-Cambridge Press, Wellesley MA, USA.
Sun S, Ma HF, Gou Y, et al., 2023. Spin- and space-multiplexing metasurface for independent phase controls of quadruplex polarization channels. Adv Opt Mater, 11(3):2202275. https://doi.org/10.1002/adom.202202275
Tsui KM, Chan SC, 2010. Pattern synthesis of narrowband conformal arrays using iterative second-order cone programming. IEEE Trans Antenn Propag, 58(6):1959–1970. https://doi.org/10.1109/TAP.2010.2046865
Wang F, Balakrishnan V, Zhou PY, et al., 2003. Optimal array pattern synthesis using semidefinite programming. IEEE Trans Signal Process, 51(5):1172–1183. https://doi.org/10.1109/TSP.2003.810308
Wu JW, Wang ZX, Fang ZQ, et al., 2020. Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces. Adv Funct Mater, 30(39):2004144. https://doi.org/10.1002/adfm.202004144
Wu JW, Wang ZX, Zhang L, et al., 2021. Anisotropic meta-surface holography in 3-D space with high resolution and efficiency. IEEE Trans Antenn Propag, 69(1):302–316. https://doi.org/10.1109/TAP.2020.3008659
Wu JW, Wang ZX, Wu RY, et al., 2023. Simple and comprehensive strategy to synthesize Huygens metasurface antenna and verification. IIEEE Trans Antenn Propag, 71(8):6652–6666. https://doi.org/10.1109/TAP.2023.3283062
Yang F, Yang SW, Chen YK, et al., 2018. Convex optimization of pencil beams through large-scale 4-D antenna arrays. IEEE Trans Antenn Propag, 66(7):3453–3462. https://doi.org/10.1109/TAP.2018.2829875
Author information
Authors and Affiliations
Contributions
Junwei WU designed the research. Junwei WU and Qiong HUA participated in the theoretical analysis and experimental designs, and drafted the paper. All the authors revised and finalized the paper.
Corresponding authors
Ethics declarations
Tie Jun CUI is the editor-in-chief of this special issue, and Qiang CHENG is an executive lead editor of this special issue; they were not involved with the peer review process of this paper. All the authors declare that they have no conflict of interest.
Additional information
Project supported by the National Key Research and Development Program of China (Nos. 2021YFA1401002 and 2018YFA070194), the National Natural Science Foundation of China (Nos. 62171124, 62288101, and 62225108), the Major Key Project of Peng Cheng Laboratory, China (No. PCL2023AS1-2), the 111 Project, China (No. 111-2-05), the Jiangsu Provincial Frontier Leading Technology Basic Research Project, China (No. BK20212002), the Fundamental Research Funds for the Central Universities, China (No. 2242023k5002), and the Jiangsu Provincial Innovation and Entrepreneurship Doctor Program, China
List of supplementary materials
1 Co-polarization patterns
2 Gain of the metasurfaces
Table S1 Summary of the peak values of the scattered patterns
Fig. S1 Co-polarization pattern of the cosecant-beam meta-surface
Fig. S2 Co-polarization pattern of the flat-top-beam meta-surface
Fig. S3 Co-polarization pattern of the double-beam meta-surface
Fig. S4 Scattered patterns of the cosecant-beam metasurface and an equal-size metal plate
Fig. S5 Scattered patterns of the flat-top-beam metasurface and an equal-size metal plate
Fig. S6 Scattered patterns of the double-beam metasurface and an equal-size metal plate
Rights and permissions
About this article
Cite this article
Wu, J., Hua, Q., Xu, H. et al. Realizing complex beams via amplitude-phase digital coding metasurfaces and semidefinite relaxation optimization. Front Inform Technol Electron Eng 24, 1708–1716 (2023). https://doi.org/10.1631/FITEE.2300146
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.2300146